09/03/2012

The Gear Seer - Understanding your Bike Drivetrain

I have never been much of a mechanic and technical knowledge of bicycles is certainly not my forte. Thus I started a site called "Bike Hacks" and not one called "Sophisticated, Reasoned, and Technically Sound Bike Modifications." One thing I have never paid much attention to are the drive trains on my bicycles. I do what I believe is the most important thing, lube the chains frequently, but truth be told, I have been riding with the same chain on one of my bikes for 16 years. I am sure the bike mechanics out there just winced when reading that last sentence.

Maybe part of my reluctance to delve into understanding drive trains is that I have always had a case of math phobia. I did okay on those elementary school math school tests I took eons ago where the teacher handed out a piece of card stock with numbers across the top and the left side of the page and there were holes cut out where you had to fill in the correct answer if you multiplied the two numbers together. I never gave myself much credit though because it was really nothing more than memorization. I did give myself credit however when I memorized the Gettysberg Address - it seemed more interesting and obviously had an impact on me because I ended up majoring in history in college. Anyway . . .

When letters were introduced into math equations my brain got confused because it thought that letters were for subjects like English and history. Even since then, math for me has been like trying to do a hilly ride on fixie . . . and segue . . .

Fortune came my way recently when we received the following message from Andrew, both a former math teacher and bike mechanic, via our Submit your Hack link -

This isn't a bike hack so much as it's a meta-bike hack. I was trying to
upgrade my Surly Cross-Check to a triple, and had to decide whether to
install a road or mountain groupset. Obviously one can go online and
plug the gearing into any number of gear ratio calculators... except
that they all output these awful tables of numbers formatted in Times
New Roman that probably haven't been updated since 1998. (One of the
calculators I found was a Java applet!)

It seems like the more natural way to display gear ratios is on a graph.
A 48/12 is the same as a 44/11, and rather than make this (un) evident
by having to cross-reference and compare numbers, why not plot front
gears on a vertical axis and rear gears on a horizontal? In that context
a gear ratio just becomes the slope of a line through the origin, and
so one can quickly SEE that the 48/12 and the 44/11 are the same.

Anyway, thinking in this vein, I whipped up a quick gear ratio visualizer.

After I read his email I got dizzy and had to close my eyes, but once I gained my balance I asked Andrew if he would write up a full post for the benefit of all. He was kind enough to write up his story and I for one now have a better understanding of how a drive train works thanks to his creation, the Gear Seer. Everything below is credited to Andrew.

* * * * * * * * * * * * * * * *

My Surly Cross-Check was showing its age.
My philosophy with bikes, as with most of life, is to use things until
they break, and then to keep on using them, until they've broken
multiple other things. “Unrideability” is my criterion for replacement,
or even for basic maintenance.

In fifteen thousand miles I had not changed the chain once. It wasn't
a huge deal. The chain had stretched a bit—all those rotations wear
away at the pins holding the links together, micron by micron—but it
still rode well and only slipped if I was really trying to book it up a
steep hill in a high gear.

Then the chain broke. I installed a new one, but I may as well have
given a heart transplant to a ninety-year-old. It just didn't work. The
stretched chain had worn the gear teeth down to daggers, and now that I
had a new, normal-sized chain, it no longer fit into the
freakishly-large gaps. If I was in the very lowest gears, I could pedal
successfully, but if I tried to do anything higher, the chain slipped.
And slipped is too generous a word: it rattled over every tooth, barely
rotating the wheel. It reminded me of driving up a hill in Quebec once
during an ice storm: the speedometer said 60 mph, but the slow passage
of the scenery said 5 mph.

I needed not just a new chain. I needed new gears.

Along with air-filled tires, gears were one of the
crucial elements that turned bicycles from an engineering curiosity to a
functional tool. In the old days of penny farthings,
there was no such thing as a gear on a bicycle. Every time you rotated
the pedals once, the wheel rotated once. In effect, the only way you
could go faster or go slower was to pedal faster or pedal slower.

But everyone who rides a bike knows that pedaling really fast
sucks, and pedaling really slow is painful. You want to pedal at a
more-or-less constant rate—you want the time it takes you to make one
pedal revolution to not always be the same time it takes the wheel to
make one revolution. Gears let you do this. Gears are like pulleys—but
for rotational rather than linear motion.

Say I'm on my Cross-Check, and I'm in the gear combination with the
front 48-toothed gear and the rear 16-toothed gear. If I turn the pedals
once, what happens? The front gear, with 48 teeth, goes around once,
and so the chain advances by 48 links. The rear gear, however, doesn't
know or care how many times the front gear has gone around—it only cares
about how much the chain wants it to move. The chain has advanced by 48
links, and so the rear gear rotates by 48 teeth. But since the rear
gear only has 16 teeth, this means that the rear gear has to rotate
three times (because 48/16 = 3. This is where the fancy word “gear
ratio” comes in: your gear ratio, in this case, is 3.) So in the 48/16
combination, you rotate the pedals once, and your rear wheel goes around
thrice.

But suppose you're in a slightly different gearing. Say you're using a
smaller chainring in front, with 36 teeth, and you're using a smaller
cog, too, with 12 teeth. This works out to being exactly the same as the
48/16 combination: every time you rotate the pedals once, the rear
wheel turns three times. (36/12 is also 3.) Of course it's not THE SAME
the same: they're totally different gears. The effect on your pedaling
is the same, but your shifters are in a different position and your
chain is touching different teeth.

In non-financial ways, the fact I needed to replace my
entire drivetrain was a welcome development. I had bought the bike in
Chicago, but now I live in San Francisco. The gears that had been nice
on Halsted Street were knee-breakers on Nob Hill. I had toyed with the
idea of adding a “granny gear”—a third, smaller front gear to help with
hills—and this was my chance.

But as soon as I started looking at options, I faced all the
paralysis of staring down 500 different kinds of peanut butter in the
supermarket. Do I get a nice Tiagra road triple, with 50-39-30-toothed
gears in the front? That's lower than my current drivetrain, and a bit
higher—I'd be able to go up steeper hills, and on the flatlands I'd be
able to faster. Or do I get a Deore triple, with 48-36-26-toothed front
gears? That gearing is way lower, so I'd be able to go up even steeper
hills. (Twin Peaks, here I come!) But it's not any faster than what I
already had. Am I happy with how fast I can currently go on the
flatlands? And what about in between? I was only thinking about the
extreme highest and lowest gears—the “edge cases,” as my programmer
friends say, or the “marginal cases,” as my economist friends say. These
thoughts racked my brain as I stared at the metaphorical wall of peanut
butter. (Which in this case was actually the Shimano website.)

How do you choose what gearing to get? Do you just calculate all the
gear ratios and think about them? What's the best way to think about
gearing? If you Google “bike gear analyzer” or the like, you can find
all sorts of online calculators that claim to help. They take in your
gearing and spit out tables and tables of numbers: gear ratios, gain
ratios, speed, splits, meters development, gear inches. I don't know
what half of these things mean. Even if I did, I doubt that looking at a
giant table of numbers would suddenly make me understand how my bike
works. It seems, as Edward Tufte
has argued, that the best way to represent huge amounts of numerical
data is with pictures. Would you rather have a list of the closing
prices of the New York Stock Exchange every day for the last year, or a
graph? Which would help you better understand the behavior of the
market? Bicycle drivetrain data is no different.

The challenge is this: suppose we have these two example gearings,
48/12 and 36/12. We want to make some sort of picture that makes it
obvious that 1) they're the SAME, because they have the same gear ratio,
but also that 2) they're DIFFERENT, because they're a physically
different combination of chain and cogs.

The gear ratio itself provides a way out. Imagine that we think of
our gear combinations as points on a two-dimensional graph, where one
axis represents the front gears and the other axis represents our rear
gears:

The awesome thing about this graph is that it contains the gear ratio in it!
Think about how we measure steepness: sometimes we measure it in
degrees (this roof has a 30º pitch), sometimes we measure it as a
percentage (10% GRADE NEXT SEVEN MILES), and sometimes we measure it as
the change in height per change in length (this pipe drops one foot
every 20 feet). If we take our graph, and we draw a line that goes up
three units for every one unit it goes over—a line that has a slope of
3—it will hit both our 48/16 combination and our 36/12 combination:

They're two distinct points—so they're different—yet they're
lying on the same line—so we can see they're the same! But why stop
there? Why not plot your entire drivetrain—why not plot every possible
gear combination?

If you tell it your wheel and tire size, it'll
even tell you how fast you'll go at a given cadence. And, you can even
compare different drivetrains—you can actually SEE, with a picture and
not just with numbers, how different gearings will affect your ability
to ride hills and flats.

Ultimately I ended up going with the Deore triple—you can see it as
one of the default drivetrains on the graph. This was partly due to the
graph, and partly due to a grueling, mountainous ride I had taken a few
weeks earlier from Palo Alto to Santa Cruz. Oh, and my old gears? Now I
have a nice new set of bottle openers, keychains, and coasters:

Actually, running a single set of drivetrain components to death is a perfectly valid way to operate. Part of the "new chain every 1000 miles" idea is inherited from roadracing teams, where it's a requirement that wheels be interchangeable. If you're not going to move a wheel between different bikes, it hardly matters if your chain and cassette mate for life.